Fourier transform ion cyclotron resonance mass-spectrometry is an established powerful experimental technique for solving a wide range of problems in analytical chemistry and biochemistry, such as determination of the composition of complex mixtures, identification of biological compounds, and accurate mass measurement. See for example Kaiser, N. K., Savory, J. J., McKenna, A. M., Quinn, J. P., Hendrickson, C. L., Marshall, A. G.: Electrically Compensated Fourier Transform Ion Cyclotron Resonance Cell for Complex Mixture Mass Analysis, Anal. Chem. 83(17), 6907-6910 (2011); Marshall, A. G., Hendrickson, C. L., Jackson, G. S.: Fourier Transform Ion Cyclotron Resonance Mass Spectrometry: a Primer, Mass Spectrum. Rev. 17(1), 1-35 (1998); Bogdanov, B., Smith, R. D.: Proteomics by FTICR Mass Spectrometry: Top Down and Bottom Up. Mass Spectrum, Rev. 24(2), 168-200 (2005); Marshall, A. G., Rodgers, R. P.: Petroleomics: The Next Grand Challenge for Chemical Analysis; Acc. Chem. Res. 37(1), 53-59 (2004); Kim, S., Kramer, R. W., Hatcher, P. G.: Graphical method for Analysis of Ultrahigh-Resolution Broadband Mass Spectra of Natural Organic Matter, the Van Krevelen Diagram, Anal. Chem. 75, 5336-5344 (2003); Nikolaev, E. N., Jertz, R., Grigoryev, A., Baykut, G.: Fine Structure in Isotopic Peak Distributions Measured Using a Dynamically Harmonized Fourier Transform Ion Cyclotron Resonance Cell at 7 T, Anal. Chem. 84(5), 2275-2283 (2012).
A main component of the ICR mass spectrometer is a measuring cell, which is a Penning ion trap in which ions are trapped by a combination of electric and magnetic fields. In order to measure the masses of the ions after they are trapped in the cell, cyclotron motion of the ions is excited by a radio frequency (RF) field and the frequency of this motion is determined by measuring the current induced in the external electric circle connected to the detection electrodes of the cell. After the Fourier transform of this time domain signal one obtains its frequency spectrum, and after calibration a mass spectrum.
The configuration of the electric field inside the ion trap strongly influences the analytical characteristics of the ICR mass spectrometer, its resolving power and mass accuracy. See Gabrielse, G., Haarsma, L., Rolston, S. L.: Open-Endcap Penning Traps for High Precision Experiments, Int. J. Mass Spectrum, Ion Processes 88, 319-332 (1989); Brustkern, A. M., Rempel, D. L., Gross, M. L.: An Electrically Compensated Trap Designed to Eighth Order for FT-ICR Mass Spectrometry, J. Am. Soc Mass Spectrum 19(9), 1281-1285 (2008). The longer the duration of an undisturbed ion current measurement, the higher is the mass resolution.
Recently performed supercomputer simulations of ion cloud motion in a Penning trap showed that the hyperbolic field is the best for achieving long duration of synchronous ion motion and obtaining high resolving power. See Nikolaev, E. N., Heeren, R. M. A., Popov, A. M., Pozdneev, A. V., Chingin, K. S.: Realistic Modeling of Ion Cloud Motion in a Fourier Transform Ion Cyclotron Resonance Cell by Use of a Particle-in-Cell Approach, Rapid Commun. Mass Spectrum. 21, 3527-3546 (2007); Nikolaev, E. N., Miluchihin, N., Inoue, M.: Evolution of an Ion Cloud in a Fourier Transform Ion Cyclotron Resonance Mass Spectrometer During Signal Detection: its Influence on Spectral Line Shape and Position. Int. J. Mass Spectrum. Ion Processes 148(3), 145-157 (1995); Vladimirov, G., Hendrickson, C. L., Blakney, G. T., Marshall, A. G., Heeren, R. M., Nikolaev, E. N.: Fourier Transform Ion Cyclotron Resonance Mass Resolution and Dynamic Range Limits Calculated by Computer Modeling of Ion Cloud Motion, J. Am. Soc. Mass Spectrum. 23(2), 375-384 (2012). Making the electric field distribution inside the FT ICR cell close to the field in a hyperbolic cell is called “cell harmonization”.
One approach to cell harmonization is based on the so-called dynamic harmonization of the electric field. See Boldin, I. A., Nikolaev, E. N.: Fourier Transform Ion Cyclotron Resonance Cell With Dynamic Harmonization of the Electric Field in the Whole Volume by Shaping of the Excitation and Detection Electrode Assembly, Rapid Commun. Mass Spectrum. 25, 122-126 (2011); see also international patent application WO 2011/045144 A1, both incorporated herein by reference. The cell field becomes hyperbolic after being averaged by the cyclotron motion. The principal design of such a cell was previously described in, which is incorporated herein by reference in its entirety, and is presented in FIG. 1A.
As described in documents identified in the preceding paragraph this cell is a cylinder segmented by curves along an axial (magnetic field) direction z
                                                                                          α                  =                                                                                                              2                          ⁢                          π                                                N                                            ⁢                      n                                        ±                                          b                      ⁡                                              (                                                  1                          -                                                                                    (                                                              z                                a                                                            )                                                        2                                                                          )                                                                                            ;                                  n                  =                  0                                            ,              1              ,              …              ⁢                                                          ,                                                N                  -                  1                                ;                                                                        b              =                                                π                  N                                -                                  π                  60                                                                                        (        1        )            Here z is the axial coordinate of the cell, a half the length of the cell, α is the angle coordinate of a point on the curve, and N the number of electrodes of each type. The original experimentally tested ion trap with dynamic harmonization had eight segments with width decreasing to the center of the cell and eight grounded electrodes with width increasing to the center, four of which are divided into two segments, each of which belongs to either excitation or detection groups of electrodes. The trapping potential V is applied to a first group of electrodes and to the trapping electrodes. Other electrodes are grounded to direct current (DC) voltage; RF voltages are applied via capacitors to the excitation groups of electrodes, and the detection group electrodes are connected with each other and with a preamplifier by capacitors of appropriate value of capacity.
The ion trap with dynamic harmonization showed the highest resolving power ever achieved on peptides and proteins. See Nikolaev, E. N., Boldin, I. A., Jertz, R., Baykut, G.: Initial Experimental Characterization of a New Ultra-High Resolution FTICR Cell With Dynamic Harmonization, J. Am. Soc. Mass Spectrum. 22(7), 1125-1133 (2011). The time of transient duration reaches 300 seconds and seems to be limited only by the vacuum inside the FT ICR cell and magnetic field inhomogeneity. See Vladimirov, G., Kostyukevich, Y., Marshall, A. G., Hendrickson, C. L., Blakney, G. T., Nikolaev, E. N.: Influence of Different Components of Magnetic Field Inhomogeneity on Cyclotron Motion Coherence at Very High Magnetic Field, Proceedings of the 58th ASMS Conference on Mass Spectrometry and Allied Topics; Salt Lake City, Utah, May (2010). Such results were obtained on a solenoid magnet of high homogeneity (less than 1 ppm of magnetic field deviation in the central region [6 cm in diameter and 6 cm length]). In order to obtain a long time domain signal using the dynamically harmonized cell on the other systems, the magnetic field of their magnets should be corrected correspondingly. Among the systems of interest are FT ICR mass spectrometers on permanent magnets, with inhomogeneity of the magnetic field about 500 ppm in a 1 cm3 cube (see Vilkov, A. N., Gamage, C. M., Misharin, A. S., Doroshenko, V. M., Tolmachev, D. A., Tarasova, I. A., Kharybin, O. N., Novoselov, K. P., Gorshkov, M. V.: Atmospheric Pressure Ionization Permanent Magnet Fourier Transform Ion Cyclotron Resonance Mass Spectrometry, J. Am. Soc. Mass Spectrum. 18(8), 1552-1558 (2007)) and on cryogenic free magnets with inhomogeneity of 100 ppm in a cylindrical volume 25 mm in diameter and 40 mm in length. These instruments demonstrated the resolving power of about 100,000 for m/z around 500. For such ICR mass spectrometers the inhomogeneity of the magnetic field is the main factor influencing the time of signal acquisition and resolving power. The inhomogeneity of the magnetic field was also the main limiting factor for an ICR mass spectrometer equipped with a 25 Tesla resistive magnet. See Shi, S. D.-H., Drader, J. J., Hendrickson, C. L., Marshall, A. G.: Fourier Transform Ion Cyclotron Resonance Mass Spectrometry in a High Homogeneity 25 Tesla Resistive Magnet, J. Am. Soc. Mass Spectrum. 10, 265-268 (1999). The inhomogeneity of the magnetic field in a sphere of 1 cm in diameter was approximately 50 ppm for this magnet. Correction of the magnetic field to achieve higher homogeneity is an expensive and complicated procedure.
Recently it was demonstrated that in the case of Gabrielse's type FT ICR cell, the influence of the inhomogeneity of the magnetic field may be decreased by compensating the electric field by accurately adjusting the compensation voltage on one of the electrodes of a seven segment cell. See Kaiser, N. K., Savory, J. J., McKenna, A. M., Quinn, J. P., Hendrickson, C. L., Marshall, A. G.: Electrically Compensated Fourier Transform Ion Cyclotron Resonance Cell for Complex Mixture Mass Analysis, Anal. Chem. 83(17), 6907-6910 (2011); Brustkern, A. M., Rempel, D. L., Gross, M. L.: An Electrically Compensated Trap Designed to Eighth Order for FT-ICR Mass Spectrometry, J. Am. Soc Mass Spectrum 19(9), 1281-1285 (2008); Tolmachev, A. V., Robinson, E. W., Wu, S., Kang, H., Lourette, N. M., Pa{hacek over (s)}a-Tolić, L., Smith, R. D.: Trapped-ion cell with improved DC potential harmonicity for FT-ICR MS, J. Am. Soc. Mass Spectrum. 19(4), 586-597 (2008).
In view of the foregoing, there is still a need for a method for the compensation of magnetic field inhomogeneities in dynamically harmonized FT ICR cells.